The controller trainee's OJI was responsible for the ATC service being provided in the Heath Point sector of Moncton ACC. The presence of the tour group in the ACC diverted the OJI's attention, and he missed the trainee controller's identification of Elite 5512 as Elite 5516. When the first officer of Elite 5516 told the controller trainee that there was another Elite, 5512, airborne, the controller should have been alerted to the possibility of an aircraft identification problem. The use of another means of aircraft identification, such as having the crew squawk ident on their transponder, would have revealed the discrepancy, and eliminated any doubt before issuing a clearance for the aircraft to climb. The controller trainee had experienced aircraft data errors on the radar display in the past, and he incorrectly assumed that the aircraft handed-off to him was the one displayed on his radar. The traffic volume and complexity at the time of the occurrence was well within the capabilities of the controller trainee to handle. The OJI felt that constant monitoring of the controller trainee was not required and might possibly decrease his confidence. It is possible that the period of light, non-complex traffic contributed to a complacent attitude in both the OJI and his controller trainee. The first officer of Elite 5516 should have transmitted the aircraft's full call sign when he acknowledged the Gander controller's instruction to change to Moncton Centre. The Gander controller probably would have heard the wrong aircraft identification, advised Elite 5516 of their error, and instructed the correct aircraft, Elite 5512, to contact Moncton ACC. Had the captain of Elite 5516 been present when the hand-off and clearance to climb were received, he may have detected the case of mistaken identity.Analysis The controller trainee's OJI was responsible for the ATC service being provided in the Heath Point sector of Moncton ACC. The presence of the tour group in the ACC diverted the OJI's attention, and he missed the trainee controller's identification of Elite 5512 as Elite 5516. When the first officer of Elite 5516 told the controller trainee that there was another Elite, 5512, airborne, the controller should have been alerted to the possibility of an aircraft identification problem. The use of another means of aircraft identification, such as having the crew squawk ident on their transponder, would have revealed the discrepancy, and eliminated any doubt before issuing a clearance for the aircraft to climb. The controller trainee had experienced aircraft data errors on the radar display in the past, and he incorrectly assumed that the aircraft handed-off to him was the one displayed on his radar. The traffic volume and complexity at the time of the occurrence was well within the capabilities of the controller trainee to handle. The OJI felt that constant monitoring of the controller trainee was not required and might possibly decrease his confidence. It is possible that the period of light, non-complex traffic contributed to a complacent attitude in both the OJI and his controller trainee. The first officer of Elite 5516 should have transmitted the aircraft's full call sign when he acknowledged the Gander controller's instruction to change to Moncton Centre. The Gander controller probably would have heard the wrong aircraft identification, advised Elite 5516 of their error, and instructed the correct aircraft, Elite 5512, to contact Moncton ACC. Had the captain of Elite 5516 been present when the hand-off and clearance to climb were received, he may have detected the case of mistaken identity. Elite 5516 acknowledged and acted on ATC instructions to change to Moncton Centre that were directed to Elite 5512. The first officer of Elite 5516 did not use his aircraft's call sign when he acknowledged the hand-off to Moncton centre. The traffic volume during the occurrence was assessed as light with normal complexity. The controller trainee did not confirm that the aircraft he saw on his radar, Elite 5512, was the aircraft with which he was communicating, Elite 5516. The controller trainee cleared Elite 5516 to climb when the aircraft was not in his area of control responsibility. A tour group in the Moncton centre distracted the OJI from his responsibility to properly monitor the controller trainee.Findings Elite 5516 acknowledged and acted on ATC instructions to change to Moncton Centre that were directed to Elite 5512. The first officer of Elite 5516 did not use his aircraft's call sign when he acknowledged the hand-off to Moncton centre. The traffic volume during the occurrence was assessed as light with normal complexity. The controller trainee did not confirm that the aircraft he saw on his radar, Elite 5512, was the aircraft with which he was communicating, Elite 5516. The controller trainee cleared Elite 5516 to climb when the aircraft was not in his area of control responsibility. A tour group in the Moncton centre distracted the OJI from his responsibility to properly monitor the controller trainee. A loss of separation occurred because the OJI was not properly monitoring the controller trainee when the trainee cleared Elite 5516 to climb. Contributing to the occurrence were the following: the trainee did not properly identify the aircraft; the first officer of Elite 5516 used improper phraseology; and, the Gander controller did not confirm the identification of the aircraft that read back the clearance.Causes and Contributing Factors A loss of separation occurred because the OJI was not properly monitoring the controller trainee when the trainee cleared Elite 5516 to climb. Contributing to the occurrence were the following: the trainee did not properly identify the aircraft; the first officer of Elite 5516 used improper phraseology; and, the Gander controller did not confirm the identification of the aircraft that read back the clearance.